R and Relevance Principle Revisited

Yang, Eunsuk

doi:10.1007/s10992-012-9247-1

Cited by 15 publications

(13 citation statements)

References 19 publications

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“…This section summarizes our work in [22]. More exactly, we briefly recall new strong and weak relevance principles introduced in [22], that is, NSRP and NWRP, because they are unfamiliar to the readers. (As we mentioned in footnote 2, we assumed that formulas such as .…”

Section: Propositional Constants and New Relevance Principlesmentioning

confidence: 99%

“…Very recently, the present author [22] introduced new strong and weak relevance principles because the principles SRP and WRP do not work on relevance systems with propositional constants (see Galatos, Jipsen, Kowalski, and Ono [11] and Restall [20]). According to him, a system is said to be strongly relevant if it satisfies the new strong relevance principle (NSRP) in [22] that ' ! is a theorem only if ' and either explicitly or strong implicitly share a propositional variable, and weakly relevant if it satisfies the new weak relevance principle (NWRP) that ' !…”

Section: Introductionmentioning

confidence: 99%

“…Let us call the relevance principles in [1] and [7] old relevance principles, and the relevance principles in [22] new relevance principles. Here, we introduce logics being both fuzzy in Cintula's sense and relevant in the old and new senses.…”

Section: Introductionmentioning

confidence: 99%

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Substructural Fuzzy-Relevance Logic

Yang¹

2015

Notre Dame J. Formal Logic

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This paper proposes a new topic in substructural logic for use in research joining the fields of relevance and fuzzy logics. For this, we consider old and new relevance principles. We first introduce fuzzy systems satisfying an old relevance principle, that is, Dunn's weak relevance principle. We present ways to obtain relevant companions of the weakening-free uninorm (based) systems introduced by Metcalfe and Montagna and fuzzy companions of the system R of relevant implication (without distributivity) and its neighbors. The algebraic structures corresponding to the systems are then defined, and completeness results are provided. We next consider fuzzy systems satisfying new relevance principles introduced by Yang. We show that the weakening-free uninorm (based) systems and some extensions and neighbors of R satisfy the new relevance principles.

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Section: Propositional Constants and New Relevance Principlesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Substructural Fuzzy-Relevance Logic

Yang¹

2015

Notre Dame J. Formal Logic

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“…32-33) and it has become since then a folklore necessary (though not sufficient) requirement for any formal system of relevant logic. The philosophical motivation behind it is quite natural: for an implication to be relevant the antecedent better have something in common with the consequent (a recent place where related issues have been studied is [12]). A solid survey where this and many other topics in relevant logic are discussed is [3].…”

Section: Introductionmentioning

confidence: 99%

Variable Sharing in Substructural Logics: an Algebraic Characterization

Badía

2018

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“…When our language has ⊥, the principle fails quite easily since ⊥ → θ (for arbitrary θ) would be a theorem, tempting one to claim that no system involving ⊥ should qualify as a system of relevant logic. However, Yang [31] has suggested recently the strong implicit relevance property as a nice substitute of the variable sharing property that would allow for systems containing ⊥. 5 See also the bi-theories in [23].…”

mentioning

confidence: 99%

Infinitary Propositional Relevant Languages With Absurdity

Badía¹

2017

The Review of Symbolic Logic

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Analogues of Scott's isomorphism theorem, Karp's theorem as well as results on lack of compactness and strong completeness are established for infinitary propositional relevant logics. An "interpolation theorem" (of a particular sort introduced by Barwise and van Benthem) for the infinitary quantificational boolean logic L8ω holds. This yields a preservation result characterizing the expressive power of infinitary relevant languages with absurdity using the model-theoretic relation of relevant directed bisimulation as well as a Beth definability property.

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R and Relevance Principle Revisited

Cited by 15 publications

References 19 publications

Substructural Fuzzy-Relevance Logic

Substructural Fuzzy-Relevance Logic

Variable Sharing in Substructural Logics: an Algebraic Characterization

Infinitary Propositional Relevant Languages With Absurdity

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